Validation Case: 3D Triaxial Displacement Secondary Creep (NAFEMS Test 6(b))

This validation case belongs to solid mechanics. The aim of this test case is to validate the following parameter:

• creep material behavior
• standard and reduced integration elements
• automatic time stepping

The simulation results were compared to the results presented in [NAFEMS]\(^1\).

Geometry

The geometry consists of a cube with edge length \(l\) = 0.1 \(m\).

The coordinates for the points in the cube geometry are as tabulated below:

	A	B	C	D	E	F	G	H
x	0	0.1	0.1	0	0	0.1	0	0.1
y	0	0	0.1	0.1	0	0	0.1	0.1
z	0	0	0	0	0.1	0.1	0.1	0.1

Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Nonlinear static

Mesh and Element Types: The meshes for cases A through D are second-order hexahedral one-element meshes. They were created locally and imported to SimScale. For cases E through H, the standard algorithm was used to generate a second-order tetrahedral mesh.

Case	Mesh Type	Number of Nodes	Creep Formulation	Element Type
A	2nd order hexahedral	20	Norton	Standard
B	2nd order hexahedral	20	Norton	Reduced integration
C	2nd order hexahedral	20	Time Hardening	Standard
D	2nd order hexahedral	20	Time Hardening	Reduced integration
E	2nd order standard	235	Norton	Standard
F	2nd order standard	235	Norton	Reduced integration
G	2nd order standard	235	Time Hardening	Standard
H	2nd order standard	235	Time Hardening	Reduced integration

Find below the standard mesh used for cases E through H:

Simulation Setup

Material:

• Steel (linear elastic)
  • Isotropic: \(E\) = 200 \(GPa\)
  • \(\nu\) = 0.3
  • \(\rho\) = 7870 \(kg/m³\)
  • Creep formulation:
    • Time hardening
      • A: 8.681e-48 \(1/s\)
      • N: 5
      • M: 0
    • Norton
      • A: 8.681e-48 \(1/s\)
      • N: 5

Boundary Conditions:

• Constraints:
  • Fixed value:
    • Face ADEH: \(d_x\) = 0 \(m\)
    • Face ABFE: \(d_y\) = 0 \(m\)
    • Face ABCD: \(d_z\) = 0 \(m\)
  • Displacement in x-direction
    • Face BCGF: \(d_x\) = 0.3 \(mm\)
  • Displacement in y-direction
    • Face CDHG: \(d_y\) = 0.2 \(mm\)
  • Displacement in z-direction
    • Face EFGH: \(d_z\) =0.1 \(mm\)

Advanced Automatic Time Stepping

For all cases, the following advanced automatic time stepping settings were defined under Simulation control:

• Retiming event: Field change
• Target field component: Internal variable V1 (accumulated unelastic strain)
• Threshold value: 0.00005
• Timestep calculation: Mixed
• Field change target: 0.00004

Result Comparison

The secondary creep movement validation is done by comparing the stress (\(\sigma_{xx}\)) after a creep time of 1000 hours. Below you will find the SimScale and reference results from [NAFEMS]\(^1\):

Case	NAFEMS R27 [MPa]	SimScale [MPa]	Error [%]
A	1007.7	1008.23	-0.053
B	1007.7	1008.23	-0.053
C	1007.7	1008.23	-0.053
D	1007.7	1008.23	-0.053
E	1007.7	1008.23	-0.053
F	1007.7	1008.23	-0.053
G	1007.7	1008.23	-0.053
H	1007.7	1008.23	-0.053

The displacement of the geometry can be seen below:

Last updated: June 27th, 2020